Third-stage turbine bucket airfoil

ABSTRACT

The third-stage buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z. The X, Y and Z values may be scaled as a function of the same constant or number to provide a scaled-up or scaled-down airfoil section for the bucket.

This invention was made with Government support under Contract No. DE-FC21-95MC31176 awarded by the Department of Energy. The Government has certain rights in this invention.

BACKGROUND OF THE INVENTION

The present invention relates to a turbine bucket for a gas turbine stage and particularly relates to a third-stage turbine bucket airfoil profile.

In recent years, advanced gas turbines have trended toward increasing firing temperatures and efforts to improve cooling of the various turbine components. In a particular gas turbine design of the assignee, a high output turbine that uses a combination of steam and air cooling to meet a 60% combined cycle efficiency is undergoing development. It will be appreciated that the design and construction of the turbine buckets and particularly the buckets of the third turbine stage of that turbine require optimized aerodynamic efficiency, as well as aerodynamic and mechanical bucket loading.

BRIEF SUMMARY OF THE INVENTION

In accordance with an embodiment of the present invention, there is provided a unique turbine bucket airfoil profile for a turbine stage, preferably the third stage, which may be defined by a unique loci of points to achieve the necessary efficiency in loading requirements whereby improved turbine performance is obtained. It will be appreciated that the nominal profile given by the X, Y, Z coordinates of Table I, which follows, define this unique loci of points. The coordinates given in inches in Table I are for a cold, i.e., room-temperature profile for each cross-section of the bucket. Each defined cross-section is joined smoothly with adjacent cross-sections to form the complete airfoil shape. It will also be appreciated that as the bucket heats up in use, the profile will change as a result of stress and temperature. Thus, the cold or room-temperature profile is given by the X, Y, Z coordinates for manufacturing purposes. Because a manufactured bucket airfoil profile may be different than the nominal airfoil profile given in the following table, a distance of ±0.160 inches from the nominal profile in a direction normal to any surface location along the nominal profile and which includes any coating process, defines the profile envelope for this design. The design is robust to this variation with impairment of the mechanical and aerodynamic functions.

It will also be appreciated that the airfoil can be scaled-up or scaled-down geometrically for introduction into other similar turbine designs. Consequently, the X, Y and Z coordinates of the nominal airfoil profile given below are a function of the same constant or number. That is, the X, Y and Z coordinate values given in the Table may be multiplied or divided by the same constant or number to provide a scaled-up or scaled-down version of the bucket airfoil profile, while retaining the airfoil section shape.

In a preferred embodiment according to the present invention, there is provided a turbine bucket having a bucket airfoil shape in an envelope within ±0.160 inches in a direction normal to any airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.

In a further preferred embodiment according to the present invention, there is provided a turbine bucket having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil bucket profile, the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.

In a further preferred embodiment according to the present invention, there is provided a turbine comprising a turbine wheel having a plurality of buckets, each of the buckets having an airfoil shape in an envelope within ±0.160 inches in a direction normal to any bucket airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.

In a further preferred embodiment according to the present invention, there is provided a turbine comprising a turbine wheel having a plurality of buckets, each of the buckets having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side elevational view of a turbine bucket including an airfoil, shank and dovetail constructed in accordance with a preferred embodiment of the present invention;

FIG. 2 is a top, leading edge and pressure side perspective view thereof;

FIG. 3 is a perspective view of the bucket as viewed along its leading edge;

FIG. 4 is a perspective view of the bucket as viewed along its trailing edge;

FIG. 5 is a top, leading edge and suction side view of the bucket hereof;

FIG. 6 is an enlarged end view of the bucket as viewed radially inwardly; and

FIG. 7 is a schematic illustration of a turbine having a third-stage turbine wheel employing the buckets hereof.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawing figures, particularly to FIGS. 1 and 2, there is illustrated a turbine blade constructed in accordance with the present invention and including an airfoil 10 mounted on a platform 12 carried by a shank 14. The radially inner end of the shank 14 carries a dovetail 16 for coupling the blade to a turbine wheel, not shown. The airfoil 10, platform 12 and dovetail 16 are collectively referred to as a bucket, generally designated 17. The airfoil 10 has a compound curvature with suction and pressure sides 18 and 20, respectively. As conventional, it will be appreciated that the dovetail 16 mates in dovetail openings in a turbine wheel. A plurality of the present third-stage buckets, preferably ninety-two buckets, are circumferentially spaced one from the other about the wheel and turbine rotor axis. Additionally, there are wheelspace seals 22, i.e., angel wings, formed on the axially forward and aft sides of shank 14. Preferably, the bucket is integrally cast with cooling, preferably air-cooling, passages, not shown, internal to the bucket including airfoil 10.

Referring now to the drawing figures, there is shown a Cartesian coordinate system for X, Y and Z values. These coordinate values are set forth in inches in Table I which follows. The Cartesian coordinate system has orthogonally-related X, Y and Z axes with the Z axis extending perpendicular to a plane normal to a radius from the centerline of the turbine rotor, i.e., normal to a plane containing the X and Y values. The Z distance commences at zero in the X, Y plane at the radially innermost aerodynamic section. The Y axis lies parallel to the turbine rotor centerline, i.e., the rotary axis. By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile of airfoil 10 can be ascertained. By connecting the X and Y values with smooth, continuing arcs, each profile section at each distance Z is fixed. The surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the airfoil. The tabular values given in Table I below are in inches and represent airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil. The sign convention assigns a positive value to the value Z and positive and negative values for the X and Y coordinates, as typically used in a Cartesian coordinate system.

The Table I values are generated and shown to three decimal places for determining the profiles of the airfoil. Further, there are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Accordingly, the values for the profile given in Table I are for a nominal airfoil. It will therefore be appreciated that ± typical manufacturing tolerances, i.e., plus or minus values and coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of ±0.160 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular bucket design and turbine.

The coordinate values given in Table I below provide the preferred nominal profile envelope.

TABLE I X Y Z 0.215 −1.756 0.000 −0.188 −1.723 0.000 −0.533 −1.498 0.000 −0.804 −1.187 0.000 −0.110 −1.751 0.000 −0.471 −1.553 0.000 −0.758 −1.255 0.000 −0.029 −1.771 0.000 −0.405 −1.603 0.000 −0.706 −1.320 0.000 −0.926 −0.970 0.000 0.342 −1.655 0.000 0.288 −1.718 0.000 0.053 −1.781 0.000 −0.335 −1.648 0.000 −0.651 −1.382 0.000 −0.886 −1.043 0.000 0.136 −1.779 0.000 −0.263 −1.688 0.000 −0.593 −1.441 0.000 −0.846 −1.115 0.000 −0.993 −0.819 0.000 0.392 −1.414 0.000 −1.062 −0.412 0.000 −0.963 −0.896 0.000 0.393 −1.331 0.000 −1.060 −0.495 0.000 0.391 −1.248 0.000 −1.053 −0.578 0.000 0.386 −1.166 0.000 −1.038 −0.659 0.000 0.371 −1.578 0.000 −1.018 −0.740 0.000 0.386 −1.497 0.000 0.368 −0.174 0.000 0.346 −0.587 0.000 0.372 −1.001 0.000 −1.002 −0.005 0.000 0.382 −0.092 0.000 0.346 −0.504 0.000 0.364 −0.918 0.000 −1.026 −0.084 0.000 −0.811 0.361 0.000 0.348 −0.422 0.000 0.357 −0.836 0.000 −1.043 −0.165 0.000 0.352 −0.339 0.000 0.352 −0.753 0.000 −0.858 0.293 0.000 −1.054 −0.247 0.000 −0.938 0.149 0.000 −0.759 0.426 0.000 0.359 −0.256 0.000 0.348 −0.670 0.000 −0.704 0.488 0.000 0.380 −1.083 0.000 −1.059 −0.330 0.000 −0.972 0.073 0.000 −0.901 0.222 0.000 0.380 1.236 0.000 0.469 0.227 0.000 −0.271 0.872 0.000 0.158 1.123 0.000 0.085 1.084 0.000 0.696 0.669 0.000 −0.402 0.771 0.000 0.499 0.304 0.000 −0.588 0.606 0.000 −0.337 0.823 0.000 0.012 1.044 0.000 0.742 0.737 0.000 −0.060 1.004 0.000 0.533 0.380 0.000 −0.202 0.919 0.000 0.398 −0.011 0.000 −0.647 0.548 0.000 0.792 0.803 0.000 0.232 1.161 0.000 0.570 0.454 0.000 0.418 0.069 0.000 −0.132 0.963 0.000 0.843 0.869 0.000 0.609 0.527 0.000 −0.465 0.718 0.000 0.442 0.149 0.000 −0.527 0.662 0.000 0.306 1.199 0.000 0.895 0.933 0.000 0.651 0.598 0.000 0.529 1.307 0.000 1.443 1.699 0.000 1.557 1.557 0.000 1.237 1.293 0.000 1.214 1.603 0.000 0.948 0.996 0.000 1.290 1.635 0.000 1.137 1.571 0.000 0.908 1.475 0.000 1.621 1.609 0.000 1.299 1.349 0.000 1.003 1.058 0.000 0.680 1.376 0.000 1.366 1.667 0.000 0.756 1.409 0.000 1.683 1.664 0.000 1.362 1.402 0.000 1.678 1.776 0.000 1.060 1.119 0.000 1.597 1.760 0.000 1.519 1.731 0.000 0.984 1.507 0.000 0.605 1.342 0.000 1.426 1.454 0.000 1.117 1.179 0.000 1.061 1.539 0.000 0.832 1.442 0.000 1.733 1.727 0.000 1.491 1.506 0.000 1.176 1.237 0.000 0.454 1.272 0.000 −0.172 −1.723 0.500 −0.529 −1.519 0.500 −0.810 −1.217 0.500 −0.092 −1.744 0.500 −0.464 −1.570 0.500 −0.760 −1.283 0.500 −0.969 −0.927 0.500 0.010 −1.755 0.500 −0.395 −1.617 0.500 −0.706 −1.346 0.500 −0.932 −1.001 0.500 0.073 −1.753 0.500 −0.324 −1.658 0.500 0.278 −1.630 0.500 −0.649 −1.406 0.500 −0.894 −1.075 0.500 0.225 −1.693 0.500 0.152 −1.731 0.500 −0.249 −1.694 0.500 −0.590 −1.464 0.500 −0.854 −1.147 0.500 0.325 −1.473 0.500 −1.002 −0.851 0.500 −1.074 −0.447 0.500 0.331 −1.390 0.500 −1.072 −0.529 0.500 0.333 −1.308 0.500 −1.063 −0.612 0.500 0.332 −1.225 0.500 −1.048 −0.693 0.500 0.328 −1.142 0.500 0.309 −1.554 0.500 −1.028 −0.773 0.500 −1.070 −0.364 0.500 −0.979 0.037 0.500 −0.764 0.389 0.500 0.331 −0.235 0.500 0.302 −0.647 0.500 0.323 −1.060 0.500 −1.009 −0.040 0.500 −0.816 0.324 0.500 0.346 −0.154 0.500 0.303 −0.564 0.500 0.317 −0.977 0.500 −1.033 −0.119 0.500 −0.863 0.256 0.500 0.363 −0.073 0.500 0.306 −0.482 0.500 0.312 −0.895 0.500 −1.050 −0.200 0.500 −0.906 0.185 0.500 −0.652 0.510 0.500 0.312 −0.399 0.500 0.307 −0.812 0.500 −1.062 −0.282 0.500 −0.944 0.112 0.500 −0.709 0.450 0.500 0.320 −0.317 0.500 0.304 −0.730 0.500 0.866 0.866 0.500 0.621 0.533 0.500 −0.469 0.677 0.500 0.436 0.164 0.500 −0.135 0.921 0.500 0.228 1.119 0.500 0.920 0.929 0.500 0.666 0.603 0.500 −0.531 0.623 0.500 0.467 0.241 0.500 −0.205 0.877 0.500 0.154 1.080 0.500 0.713 0.671 0.500 −0.592 0.567 0.500 0.501 0.316 0.500 −0.273 0.830 0.500 0.081 1.042 0.500 0.762 0.738 0.500 0.539 0.390 0.500 −0.340 0.781 0.500 0.384 0.007 0.500 0.009 1.002 0.500 0.375 1.193 0.500 0.813 0.802 0.500 0.579 0.462 0.500 −0.405 0.730 0.500 0.409 0.086 0.500 −0.064 0.962 0.500 0.301 1.156 0.500 0.599 1.300 0.500 0.978 1.465 0.500 1.359 1.625 0.500 1.747 1.762 0.500 1.527 1.487 0.500 1.208 1.225 0.500 0.524 1.265 0.500 0.902 1.433 0.500 1.283 1.594 0.500 1.666 1.749 0.500 1.593 1.538 0.500 1.270 1.280 0.500 0.975 0.991 0.500 0.450 1.229 0.500 0.826 1.400 0.500 1.207 1.562 0.500 1.588 1.721 0.500 1.658 1.589 0.500 1.333 1.334 0.500 1.031 1.051 0.500 0.750 1.367 0.500 1.131 1.530 0.500 1.512 1.689 0.500 1.721 1.642 0.500 1.397 1.386 0.500 1.089 1.110 0.500 0.675 1.334 0.500 1.054 1.497 0.500 1.436 1.657 0.500 1.781 1.699 0.500 1.462 1.437 0.500 1.143 1.168 0.500 −0.943 −1.035 1.000 −0.706 −1.371 1.000 0.215 −1.605 1.000 −0.385 −1.628 1.000 0.009 −1.728 1.000 −0.978 −0.961 1.000 −0.762 −1.310 1.000 −0.456 −1.585 1.000 −0.073 −1.729 1.000 −1.010 −0.885 1.000 −0.814 −1.246 1.000 −0.524 −1.538 1.000 −0.155 −1.717 1.000 −0.862 −1.179 1.000 −0.588 −1.487 1.000 −0.234 −1.695 1.000 −0.905 −1.109 1.000 −0.649 −1.430 1.000 −0.311 −1.665 1.000 0.089 −1.707 1.000 0.161 −1.667 1.000 −1.075 −0.646 1.000 0.272 −1.202 1.000 −1.085 −0.564 1.000 0.273 −1.284 1.000 −1.088 −0.482 1.000 0.271 −1.367 1.000 −1.085 −0.400 1.000 −1.038 −0.807 1.000 0.264 −1.449 1.000 −1.060 −0.727 1.000 0.248 −1.530 1.000 0.268 −1.119 1.000 −0.659 0.470 1.000 −0.912 0.147 1.000 −1.061 −0.236 1.000 0.255 −0.790 1.000 0.274 −0.378 1.000 −0.599 0.527 1.000 −0.869 0.217 1.000 −1.042 −0.156 1.000 0.256 −0.872 1.000 0.264 −0.460 1.000 0.345 −0.056 1.000 −0.822 0.285 1.000 −1.018 −0.077 1.000 0.259 −0.955 1.000 0.258 −0.542 1.000 0.322 −0.135 1.000 −0.771 0.349 1.000 −0.988 0.000 1.000 0.263 −1.037 1.000 0.255 −0.624 1.000 0.303 −0.215 1.000 −0.716 0.411 1.000 −0.952 0.074 1.000 −1.075 −0.318 1.000 0.254 −0.707 1.000 0.287 −0.296 1.000 0.400 0.100 1.000 −0.344 0.738 1.000 0.588 0.467 1.000 0.834 0.798 1.000 0.443 1.187 1.000 0.076 0.999 1.000 0.371 0.023 1.000 −0.278 0.786 1.000 0.545 0.396 1.000 0.781 0.734 1.000 0.148 1.038 1.000 −0.209 0.833 1.000 0.504 0.324 1.000 −0.537 0.582 1.000 0.730 0.669 1.000 0.222 1.076 1.000 −0.140 0.877 1.000 0.467 0.251 1.000 −0.474 0.636 1.000 0.681 0.603 1.000 0.944 0.921 1.000 0.295 1.114 1.000 −0.069 0.920 1.000 0.432 0.176 1.000 −0.410 0.687 1.000 0.634 0.536 1.000 0.889 0.860 1.000 0.369 1.151 1.000 0.003 0.960 1.000 1.117 1.098 1.000 1.430 1.367 1.000 1.758 1.616 1.000 1.579 1.679 1.000 1.198 1.519 1.000 0.819 1.358 1.000 1.058 1.040 1.000 1.365 1.316 1.000 1.694 1.565 1.000 1.655 1.711 1.000 1.275 1.551 1.000 0.894 1.391 1.000 0.518 1.222 1.000 1.001 0.981 1.000 1.301 1.263 1.000 1.628 1.516 1.000 1.733 1.739 1.000 1.351 1.583 1.000 0.970 1.423 1.000 0.593 1.257 1.000 1.239 1.209 1.000 1.562 1.466 1.000 1.813 1.742 1.000 1.427 1.615 1.000 1.046 1.455 1.000 0.668 1.291 1.000 1.178 1.154 1.000 1.495 1.417 1.000 1.821 1.670 1.000 1.503 1.647 1.000 1.122 1.487 1.000 0.743 1.325 1.000 −0.943 −1.035 1.000 −0.706 −1.371 1.000 0.215 −1.605 1.000 −0.385 −1.628 1.000 0.009 −1.728 1.000 −0.978 −0.961 1.000 −0.762 −1.310 1.000 −0.456 −1.585 1.000 −0.073 −1.729 1.000 −1.010 −0.885 1.000 −0.814 −1.246 1.000 −0.524 −1.538 1.000 −0.155 −1.717 1.000 −0.862 −1.179 1.000 −0.588 −1.487 1.000 −0.234 −1.695 1.000 −0.905 −1.109 1.000 −0.649 −1.430 1.000 −0.311 −1.665 1.000 0.089 −1.707 1.000 0.161 −1.667 1.000 −1.075 −0.646 1.000 0.272 −1.202 1.000 −1.085 −0.564 1.000 0.273 −1.284 1.000 −1.088 −0.482 1.000 0.271 −1.367 1.000 −1.085 −0.400 1.000 −1.038 −0.807 1.000 0.264 −1.449 1.000 −1.060 −0.727 1.000 0.248 −1.530 1.000 0.268 −1.119 1.000 −0.659 0.470 1.000 −0.912 0.147 1.000 −1.061 −0.236 1.000 0.255 −0.790 1.000 0.274 −0.378 1.000 −0.599 0.527 1.000 −0.869 0.217 1.000 −1.042 −0.156 1.000 0.256 −0.872 1.000 0.264 −0.460 1.000 0.345 −0.056 1.000 −0.822 0.285 1.000 −1.018 −0.077 1.000 0.259 −0.955 1.000 0.258 −0.542 1.000 0.322 −0.135 1.000 −0.771 0.349 1.000 −0.988 0.000 1.000 0.263 −1.037 1.000 0.255 −0.624 1.000 0.303 −0.215 1.000 −0.716 0.411 1.000 −0.952 0.074 1.000 −1.075 −0.318 1.000 0.254 −0.707 1.000 0.287 −0.296 1.000 0.400 0.100 1.000 −0.344 0.738 1.000 0.588 0.467 1.000 0.834 0.798 1.000 0.443 1.187 1.000 0.076 0.999 1.000 0.371 0.023 1.000 −0.278 0.786 1.000 0.545 0.396 1.000 0.781 0.734 1.000 0.148 1.038 1.000 −0.209 0.833 1.000 0.504 0.324 1.000 −0.537 0.582 1.000 0.730 0.669 1.000 0.222 1.076 1.000 −0.140 0.877 1.000 0.467 0.251 1.000 −0.474 0.636 1.000 0.681 0.603 1.000 0.944 0.921 1.000 0.295 1.114 1.000 −0.069 0.920 1.000 0.432 0.176 1.000 −0.410 0.687 1.000 0.634 0.536 1.000 0.889 0.860 1.000 0.369 1.151 1.000 0.003 0.960 1.000 1.117 1.098 1.000 1.430 1.367 1.000 1.758 1.616 1.000 1.579 1.679 1.000 1.198 1.519 1.000 0.819 1.358 1.000 1.058 1.040 1.000 1.365 1.316 1.000 1.694 1.565 1.000 1.655 1.711 1.000 1.275 1.551 1.000 0.894 1.391 1.000 0.518 1.222 1.000 1.001 0.981 1.000 1.301 1.263 1.000 1.628 1.516 1.000 1.733 1.739 1.000 1.351 1.583 1.000 0.970 1.423 1.000 0.593 1.257 1.000 1.239 1.209 1.000 1.562 1.466 1.000 1.813 1.742 1.000 1.427 1.615 1.000 1.046 1.455 1.000 0.668 1.291 1.000 1.178 1.154 1.000 1.495 1.417 1.000 1.821 1.670 1.000 1.503 1.647 1.000 1.122 1.487 1.000 0.743 1.325 1.000 −0.817 −1.275 1.500 −1.022 −0.920 1.500 −0.055 −1.703 1.500 0.097 −1.642 1.500 −0.447 −1.597 1.500 0.151 −1.581 1.500 −0.763 −1.337 1.500 −0.991 −0.996 1.500 0.025 −1.682 1.500 −0.374 −1.635 1.500 0.185 −1.506 1.500 −0.707 −1.397 1.500 −0.955 −1.070 1.500 −0.297 −1.666 1.500 −0.647 −1.453 1.500 −0.914 −1.141 1.500 −0.218 −1.689 1.500 −0.583 −1.506 1.500 −0.868 −1.209 1.500 −1.050 −0.842 1.500 −0.137 −1.702 1.500 −0.516 −1.554 1.500 −1.103 −0.518 1.500 0.210 −1.179 1.500 −1.099 −0.600 1.500 0.206 −1.097 1.500 −1.089 −0.682 1.500 0.201 −1.015 1.500 0.203 −1.426 1.500 −1.072 −0.763 1.500 −1.091 −0.354 1.500 0.211 −1.344 1.500 −1.101 −0.436 1.500 0.212 −1.262 1.500 −1.031 −0.115 1.500 −0.831 0.244 1.500 0.235 −0.358 1.500 0.199 −0.768 1.500 −1.056 −0.193 1.500 −0.879 0.177 1.500 −0.608 0.486 1.500 0.252 −0.277 1.500 0.201 −0.685 1.500 −1.076 −0.273 1.500 −0.923 0.107 1.500 −0.668 0.429 1.500 0.274 −0.198 1.500 0.205 −0.603 1.500 −0.964 0.036 1.500 −0.725 0.370 1.500 0.298 −0.119 1.500 0.211 −0.521 1.500 0.199 −0.932 1.500 −1.000 −0.039 1.500 −0.780 0.308 1.500 0.325 −0.041 1.500 0.221 −0.439 1.500 0.198 −0.850 1.500 0.798 0.726 1.500 −0.547 0.541 1.500 0.550 0.398 1.500 −0.217 0.787 1.500 0.356 0.035 1.500 0.139 0.994 1.500 0.507 1.178 1.500 0.852 0.788 1.500 0.596 0.466 1.500 −0.286 0.741 1.500 0.389 0.110 1.500 0.066 0.956 1.500 0.433 1.143 1.500 0.908 0.849 1.500 0.644 0.533 1.500 −0.353 0.694 1.500 0.425 0.184 1.500 −0.006 0.916 1.500 0.359 1.107 1.500 0.965 0.908 1.500 0.693 0.599 1.500 −0.419 0.644 1.500 0.464 0.257 1.500 −0.078 0.875 1.500 0.285 1.070 1.500 0.745 0.663 1.500 −0.484 0.593 1.500 0.506 0.328 1.500 −0.148 0.832 1.500 0.212 1.033 1.500 1.718 1.698 1.500 1.724 1.538 1.500 1.393 1.293 1.500 1.082 1.024 1.500 0.883 1.347 1.500 1.262 1.508 1.500 1.642 1.667 1.500 1.790 1.588 1.500 1.458 1.344 1.500 1.142 1.080 1.500 0.807 1.314 1.500 1.186 1.476 1.500 1.566 1.635 1.500 1.855 1.638 1.500 1.524 1.393 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0.952 0.368 12.500 0.601 0.203 12.500 0.241 0.498 12.500 0.609 0.620 12.500 0.979 0.735 12.500 1.375 0.562 12.500 1.022 0.400 12.500 0.671 0.236 12.500 0.168 0.472 12.500 0.535 0.596 12.500 0.905 0.713 12.500 1.277 0.822 12.500 1.445 0.595 12.500 1.093 0.433 12.500 0.741 0.269 12.500 0.095 0.446 12.500 0.462 0.572 12.500 0.831 0.690 12.500 1.203 0.801 12.500 1.516 0.627 12.500 1.501 0.885 12.500 1.875 0.987 12.500 2.237 1.033 12.500 1.938 0.822 12.500 1.427 0.864 12.500 1.800 0.967 12.500 2.175 1.068 12.500 2.008 0.856 12.500 1.657 0.692 12.500 1.352 0.843 12.500 1.726 0.947 12.500 2.100 1.048 12.500 2.077 0.891 12.500 1.727 0.724 12.500 1.651 0.926 12.500 2.025 1.028 12.500 2.146 0.926 12.500 1.798 0.757 12.500 1.576 0.906 12.500 1.950 1.008 12.500 2.214 0.964 12.500 1.868 0.789 12.500 −0.576 −0.462 13.000 −1.319 −0.279 13.000 −1.556 −0.584 13.000 −1.180 −1.061 13.000 −1.621 −0.960 13.000 −0.932 −0.762 13.000 −0.639 −0.507 13.000 −1.441 −1.193 13.000 −1.260 −0.229 13.000 −1.519 −0.515 13.000 −1.232 −1.118 13.000 −1.627 −0.883 13.000 −0.985 −0.819 13.000 −0.701 −0.554 13.000 −1.199 −0.181 13.000 −1.476 −0.451 13.000 −1.293 −1.167 13.000 −1.624 −0.805 13.000 −1.036 −0.878 13.000 −1.511 −1.160 13.000 −0.762 −0.603 13.000 −1.428 −0.390 13.000 −1.364 −1.196 13.000 −1.611 −0.729 13.000 −1.085 −0.938 13.000 −1.563 −1.103 13.000 −0.821 −0.654 13.000 −1.375 −0.333 13.000 −1.588 −0.655 13.000 −1.132 −0.999 13.000 −1.600 −1.035 13.000 −0.877 −0.707 13.000 −0.247 −0.256 13.000 0.094 −0.069 13.000 0.441 0.105 13.000 0.063 0.411 13.000 −0.301 0.276 13.000 −0.660 0.126 13.000 −1.005 −0.052 13.000 −0.314 −0.296 13.000 0.025 −0.105 13.000 0.371 0.071 13.000 −0.229 0.304 13.000 −0.589 0.158 13.000 −0.937 −0.013 13.000 −0.380 −0.336 13.000 −0.044 −0.142 13.000 0.302 0.036 13.000 −0.156 0.332 13.000 −0.517 0.189 13.000 −0.869 0.024 13.000 −0.446 −0.377 13.000 −0.112 −0.179 13.000 0.232 0.002 13.000 0.581 0.172 13.000 −0.083 0.359 13.000 −0.446 0.219 13.000 −0.800 0.060 13.000 −1.136 −0.135 13.000 −0.511 −0.419 13.000 −0.180 −0.217 13.000 0.163 −0.033 13.000 0.511 0.138 13.000 −0.010 0.385 13.000 −0.374 0.248 13.000 −0.730 0.094 13.000 −1.071 −0.093 13.000 1.174 0.764 13.000 0.801 0.654 13.000 0.431 0.536 13.000 0.792 0.271 13.000 1.146 0.432 13.000 1.499 0.593 13.000 1.248 0.785 13.000 0.875 0.676 13.000 0.505 0.560 13.000 0.136 0.437 13.000 0.722 0.238 13.000 1.075 0.400 13.000 1.428 0.561 13.000 1.323 0.807 13.000 0.950 0.699 13.000 0.579 0.584 13.000 0.210 0.462 13.000 0.651 0.205 13.000 1.004 0.368 13.000 1.358 0.529 13.000 1.024 0.721 13.000 0.653 0.608 13.000 0.283 0.487 13.000 0.933 0.336 13.000 1.287 0.497 13.000 1.641 0.658 13.000 1.099 0.743 13.000 0.727 0.631 13.000 0.357 0.512 13.000 0.863 0.303 13.000 1.216 0.465 13.000 1.570 0.625 13.000 1.853 0.754 13.000 2.203 0.923 13.000 1.998 0.991 13.000 1.623 0.889 13.000 1.782 0.722 13.000 2.133 0.888 13.000 2.073 1.011 13.000 1.698 0.910 13.000 1.711 0.690 13.000 2.063 0.854 13.000 2.148 1.031 13.000 1.772 0.930 13.000 1.398 0.827 13.000 1.993 0.820 13.000 2.223 1.039 13.000 1.848 0.950 13.000 1.473 0.848 13.000 1.923 0.787 13.000 2.256 0.976 13.000 1.923 0.971 13.000 1.548 0.869 13.000 −1.131 −0.935 13.500 −1.616 −1.063 13.500 −0.855 −0.661 13.500 −1.353 −0.310 13.500 −1.593 −0.613 13.500 −1.182 −0.994 13.500 −1.646 −0.991 13.500 −0.914 −0.712 13.500 −0.605 −0.474 13.500 −1.294 −0.259 13.500 −1.555 −0.545 13.500 −1.234 −1.052 13.500 −1.659 −0.914 13.500 −0.970 −0.766 13.500 −0.670 −0.518 13.500 −1.232 −0.212 13.500 −1.512 −0.481 13.500 −1.290 −1.107 13.500 −1.658 −0.837 13.500 −1.025 −0.821 13.500 −0.733 −0.564 13.500 −1.168 −0.167 13.500 −1.463 −0.420 13.500 −1.353 −1.152 13.500 −1.646 −0.760 13.500 −1.079 −0.878 13.500 −1.570 −1.125 13.500 −0.795 −0.611 13.500 −1.504 −1.165 13.500 −1.410 −0.363 13.500 −1.427 −1.175 13.500 −1.624 −0.685 13.500 −0.540 −0.432 13.500 −0.204 −0.235 13.500 0.143 −0.057 13.500 0.495 0.110 13.500 0.037 0.376 13.500 −0.329 0.242 13.500 −0.689 0.093 13.500 −1.036 −0.084 13.500 −0.272 −0.272 13.500 0.073 −0.092 13.500 0.424 0.077 13.500 0.110 0.402 13.500 −0.256 0.270 13.500 −0.618 0.125 13.500 −0.968 −0.046 13.500 −0.340 −0.311 13.500 0.003 −0.126 13.500 0.354 0.044 13.500 −0.183 0.297 13.500 −0.546 0.155 13.500 −0.900 −0.009 13.500 −0.407 −0.350 13.500 −0.066 −0.162 13.500 0.283 0.010 13.500 −0.110 0.324 13.500 −0.474 0.185 13.500 −0.830 0.026 13.500 −0.474 −0.390 13.500 −0.135 −0.198 13.500 0.213 −0.023 13.500 0.565 0.143 13.500 −0.037 0.350 13.500 −0.402 0.214 13.500 −0.760 0.060 13.500 −1.103 −0.124 13.500 1.151 0.729 13.500 0.777 0.619 13.500 0.406 0.501 13.500 0.848 0.274 13.500 1.204 0.434 13.500 1.559 0.593 13.500 1.226 0.750 13.500 0.852 0.641 13.500 0.480 0.525 13.500 0.778 0.241 13.500 1.133 0.402 13.500 1.488 0.561 13.500 1.301 0.771 13.500 0.927 0.664 13.500 0.554 0.549 13.500 0.184 0.427 13.500 0.707 0.209 13.500 1.062 0.370 13.500 1.417 0.529 13.500 1.376 0.792 13.500 1.001 0.686 13.500 0.628 0.573 13.500 0.258 0.452 13.500 0.636 0.176 13.500 0.990 0.338 13.500 1.346 0.498 13.500 1.076 0.707 13.500 0.703 0.596 13.500 0.332 0.477 13.500 1.275 0.466 13.500 1.630 0.625 13.500 0.919 0.306 13.500 1.902 0.936 13.500 1.526 0.834 13.500 1.914 0.755 13.500 2.264 0.924 13.500 1.978 0.956 13.500 1.601 0.854 13.500 1.843 0.722 13.500 2.197 0.886 13.500 2.053 0.976 13.500 1.677 0.875 13.500 1.772 0.690 13.500 2.126 0.852 13.500 2.128 0.996 13.500 1.752 0.895 13.500 1.701 0.658 13.500 2.056 0.820 13.500 2.204 1.016 13.500 1.827 0.916 13.500 1.451 0.813 13.500 1.985 0.787 13.500 2.273 0.995 13.500 −0.884 −0.666 14.000 −1.662 −1.109 14.000 −1.173 −0.930 14.000 −1.626 −0.641 14.000 −1.485 −1.150 14.000 −1.382 −0.339 14.000 −1.561 −1.133 14.000 −0.822 −0.618 14.000 −1.623 −1.086 14.000 −1.117 −0.875 14.000 −1.657 −0.713 14.000 −1.409 −1.133 14.000 −1.440 −0.391 14.000 −1.128 −0.156 14.000 −0.759 −0.572 14.000 −1.061 −0.820 14.000 −1.679 −0.788 14.000 −1.343 −1.092 14.000 −1.494 −0.448 14.000 −1.194 −0.198 14.000 −0.694 −0.527 14.000 −1.003 −0.767 14.000 −1.689 −0.866 14.000 −1.283 −1.040 14.000 −1.543 −0.509 14.000 −1.259 −0.242 14.000 −0.629 −0.484 14.000 −0.944 −0.715 14.000 −1.684 −0.944 14.000 −1.228 −0.985 14.000 −1.588 −0.573 14.000 −1.321 −0.289 14.000 −0.563 −0.442 14.000 −1.061 −0.116 14.000 −0.711 0.060 14.000 −0.349 0.209 14.000 0.019 0.342 14.000 0.556 0.120 14.000 0.200 −0.043 14.000 −0.153 −0.213 14.000 −0.496 −0.401 14.000 −0.782 0.027 14.000 −0.422 0.181 14.000 −0.055 0.316 14.000 0.627 0.152 14.000 0.271 −0.011 14.000 −0.083 −0.178 14.000 −0.429 −0.361 14.000 −0.853 −0.006 14.000 −0.495 0.152 14.000 −0.129 0.290 14.000 0.342 0.022 14.000 −0.013 −0.143 14.000 −0.360 −0.323 14.000 −0.923 −0.041 14.000 −0.567 0.122 14.000 −0.202 0.263 14.000 0.167 0.393 14.000 0.414 0.055 14.000 0.058 −0.109 14.000 −0.292 −0.285 14.000 −0.992 −0.078 14.000 −0.639 0.091 14.000 −0.276 0.236 14.000 0.093 0.368 14.000 0.485 0.087 14.000 0.129 −0.076 14.000 −0.223 −0.248 14.000 1.629 0.596 14.000 1.271 0.438 14.000 0.913 0.281 14.000 0.390 0.467 14.000 0.764 0.585 14.000 1.139 0.696 14.000 1.701 0.628 14.000 1.343 0.470 14.000 0.985 0.312 14.000 0.316 0.442 14.000 0.689 0.562 14.000 1.064 0.674 14.000 1.441 0.781 14.000 1.415 0.501 14.000 1.056 0.344 14.000 0.699 0.185 14.000 0.242 0.418 14.000 0.614 0.539 14.000 0.989 0.652 14.000 1.365 0.760 14.000 1.486 0.533 14.000 1.128 0.375 14.000 0.770 0.217 14.000 0.539 0.515 14.000 0.914 0.630 14.000 1.290 0.739 14.000 1.558 0.565 14.000 1.200 0.407 14.000 0.841 0.249 14.000 0.465 0.491 14.000 0.838 0.608 14.000 1.214 0.717 14.000 1.592 0.822 14.000 1.970 0.924 14.000 2.319 0.943 14.000 1.987 0.757 14.000 1.516 0.801 14.000 1.894 0.904 14.000 2.273 0.998 14.000 2.058 0.788 14.000 1.818 0.883 14.000 2.197 0.983 14.000 2.130 0.820 14.000 1.772 0.660 14.000 1.743 0.863 14.000 2.121 0.964 14.000 2.201 0.852 14.000 1.844 0.692 14.000 1.667 0.843 14.000 2.045 0.944 14.000 2.272 0.886 14.000 1.915 0.725 14.000 −1.449 −1.114 14.392 −1.601 −1.103 14.392 −1.380 −1.076 14.392 −1.693 −0.981 14.392 −1.201 −0.923 14.392 −1.660 −1.052 14.392 −1.574 −0.543 14.392 −1.704 −0.826 14.392 −1.526 −1.126 14.392 −1.686 −0.749 14.392 −1.259 −0.976 14.392 −1.707 −0.904 14.392 −1.318 −1.028 14.392 −1.657 −0.676 14.392 −1.619 −0.607 14.392 −0.901 −0.668 14.392 −1.024 −0.766 14.392 −1.351 −0.322 14.392 −0.963 −0.716 14.392 −1.524 −0.482 14.392 −1.470 −0.424 14.392 −1.288 −0.275 14.392 −1.412 −0.371 14.392 −1.142 −0.870 14.392 −0.837 −0.621 14.392 −1.084 −0.817 14.392 −1.223 −0.230 14.392 −0.575 −0.448 14.392 −0.950 −0.074 14.392 −0.708 −0.532 14.392 −0.642 −0.489 14.392 −0.507 −0.408 14.392 −1.089 −0.148 14.392 −0.879 −0.039 14.392 −0.808 −0.005 14.392 −1.020 −0.110 14.392 −0.773 −0.576 14.392 −0.439 −0.368 14.392 −0.737 0.027 14.392 −0.157 −0.188 14.392 −0.231 −0.256 14.392 −0.301 −0.293 14.392 0.052 −0.119 14.392 −0.373 0.177 14.392 −0.370 −0.330 14.392 −0.592 0.090 14.392 −0.019 −0.152 14.392 −0.090 −0.186 14.392 −0.446 0.149 14.392 −0.299 0.205 14.392 −0.665 0.059 14.392 −0.519 0.120 14.392 −0.161 −0.221 14.392 0.627 0.139 14.392 0.124 −0.086 14.392 0.483 0.075 14.392 0.411 0.043 14.392 −0.151 0.259 14.392 0.072 0.337 14.392 0.555 0.107 14.392 0.146 0.362 14.392 0.339 0.010 14.392 0.221 0.387 14.392 −0.003 0.311 14.392 0.371 0.436 14.392 −0.077 0.285 14.392 −0.225 0.232 14.392 0.268 −0.022 14.392 0.196 −0.054 14.392 0.296 0.412 14.392 0.915 0.266 14.392 0.843 0.234 14.392 1.204 0.390 14.392 0.896 0.601 14.392 0.771 0.202 14.392 1.132 0.359 14.392 0.670 0.532 14.392 0.972 0.623 14.392 0.746 0.555 14.392 0.445 0.461 14.392 0.699 0.171 14.392 1.060 0.328 14.392 0.821 0.578 14.392 0.987 0.297 14.392 0.595 0.509 14.392 0.520 0.485 14.392 1.783 0.639 14.392 1.277 0.421 14.392 1.638 0.577 14.392 1.123 0.667 14.392 1.274 0.711 14.392 1.566 0.545 14.392 1.654 0.815 14.392 1.199 0.689 14.392 1.350 0.732 14.392 1.494 0.514 14.392 1.426 0.753 14.392 1.421 0.483 14.392 1.502 0.774 14.392 1.047 0.646 14.392 1.349 0.452 14.392 1.710 0.608 14.392 1.578 0.795 14.392 2.351 0.904 14.392 2.034 0.917 14.392 2.287 0.861 14.392 2.110 0.937 14.392 1.730 0.836 14.392 1.855 0.671 14.392 2.215 0.828 14.392 2.186 0.957 14.392 1.927 0.703 14.392 1.806 0.856 14.392 1.999 0.734 14.392 2.143 0.797 14.392 2.262 0.977 14.392 1.882 0.877 14.392 2.071 0.766 14.392 2.338 0.974 14.392 1.958 0.897 14.392

It will also be appreciated that the airfoil disclosed in the above Table may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil section shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values multiplied or divided by the same constant or number.

Referring now to FIG. 7, there is illustrated a turbine in which the turbine bucket having the airfoil defined herein may be utilized. In the illustrated turbine, the turbine rotor, designated 40, has first, second, third and fourth-stage rotor wheels 42, 44, 46 and 48 mounting buckets which, in conjunction with respective stator vanes 41, 43, 45 and 47, form the various stages of the rotor. Particularly, the third stage comprises a third-stage rotor wheel 46 on which the airfoils 10 hereof are mounted in opposition to third-stage stator vanes 45. It will be appreciated that a plurality of the airfoils 10 are spaced circumferentially one from the other about the third-stage wheel 46 and, in this instance, there are ninety-two buckets mounted on the third-stage wheel 46.

While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. 

What is claimed is:
 1. A turbine bucket having a bucket airfoil shape in an envelope within ±0.160 inches in a direction normal to any airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
 2. A turbine bucket according to claim 1 forming part of a third stage of a turbine.
 3. A turbine bucket having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil bucket profile; the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.
 4. A turbine bucket according to claim 3 forming part of a third stage of a turbine.
 5. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets having an airfoil shape in an envelope within ±0.160 inches in a direction normal to any bucket airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.
 6. A turbine according to claim 5 wherein the turbine wheel comprises a third-stage turbine.
 7. A turbine according to claim 5 wherein the turbine wheel has ninety-two buckets and Y represents a distance parallel to a long axis of the turbine wheel.
 8. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinates values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinates defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape; the X and Y values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.
 9. A turbine according to claim 8 wherein the turbine wheel comprises a third stage of the turbine.
 10. A turbine according to claim 8 wherein the turbine wheel has ninety-two buckets and Y represents a distance parallel to a long axis of the turbine wheel. 